Question: Which of the following numbers is a factor of 120? ${7,9,11,12,14}$
By definition, a factor of a number will divide evenly into that number. We can start by dividing $120$ by each of our answer choices. $120 \div 7 = 17\text{ R }1$ $120 \div 9 = 13\text{ R }3$ $120 \div 11 = 10\text{ R }10$ $120 \div 12 = 10$ $120 \div 14 = 8\text{ R }8$ The only answer choice that divides into $120$ with no remainder is $12$ $ 10$ $12$ $120$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $12$ are contained within the prime factors of $120$ $120 = 2\times2\times2\times3\times5 12 = 2\times2\times3$ Therefore the only factor of $120$ out of our choices is $12$. We can say that $120$ is divisible by $12$.